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From "Daniel Kuan (JIRA)" <j...@apache.org>
Subject [jira] Updated: (MATH-216) Faster and more computationally-efficient Fast Fourier Transform implementation
Date Fri, 11 Jul 2008 19:06:33 GMT

     [ https://issues.apache.org/jira/browse/MATH-216?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
]

Daniel Kuan updated MATH-216:
-----------------------------

    Description: 
Here are some suggestions on improving the speed and computational-efficiency of FastFourierTransformer.

1. Store roots of unity as a double array of arrays instead of Complex array.

No need for all the functionality that comes with class Complex when all that is required
are the values of the roots of unity.

2. Keep track of the largest set of roots of unity calculated so far, and adopt Singleton
pattern.

Subsequent requests for smaller sets of roots of unity can be derived from the largest set
-- no need to recalculate the roots of unity from scratch.

3. When computing the nth roots of unity, need only compute n/4 roots instead of all n roots.

Since the roots of unity lie along a circle of unity radius, trigonometric relations can be
leveraged to reduce the number of roots that need to be computed from n to n/4.

4. Execute transform algorithm on double primitives instead of on class Complex.

New instances of Complex are instantiated each time a simple arithmetic operation is performed
on the Complex variables. Much time is lost to object creation and initialisation.


  was:
Here are some suggestions on improving the speed and computational-efficiency of FastFourierTransformer.

1. Store roots of unity as a double array of arrays instead of Complex array.

No need for all the functionality that comes with class Complex when all that is required
are the values of the roots of unity.

2. Keep track of the largest set of roots of unity calculated so far.

Subsequent requests for smaller sets of roots of unity can be derived from the largest set
-- no need to recalculate the roots of unity from scratch.

3. When computing the nth roots of unity, need only compute n/4 roots instead of all n roots.

Since the roots of unity lie along a circle of unity radius, trigonometric relations can be
leveraged to reduce the number of roots that need to be computed from n to n/4.

4. Execute transform algorithm on double primitives instead of on class Complex.

New instances of Complex are instantiated each time a simple arithmetic operation is performed
on the Complex variables. Much time is lost to object creation and initialisation.




Modified suggestion #2: added "adopt Singleton pattern".

> Faster and more computationally-efficient Fast Fourier Transform implementation
> -------------------------------------------------------------------------------
>
>                 Key: MATH-216
>                 URL: https://issues.apache.org/jira/browse/MATH-216
>             Project: Commons Math
>          Issue Type: Improvement
>    Affects Versions: 1.2
>            Reporter: Daniel Kuan
>            Priority: Minor
>
> Here are some suggestions on improving the speed and computational-efficiency of FastFourierTransformer.
> 1. Store roots of unity as a double array of arrays instead of Complex array.
> No need for all the functionality that comes with class Complex when all that is required
are the values of the roots of unity.
> 2. Keep track of the largest set of roots of unity calculated so far, and adopt Singleton
pattern.
> Subsequent requests for smaller sets of roots of unity can be derived from the largest
set -- no need to recalculate the roots of unity from scratch.
> 3. When computing the nth roots of unity, need only compute n/4 roots instead of all
n roots.
> Since the roots of unity lie along a circle of unity radius, trigonometric relations
can be leveraged to reduce the number of roots that need to be computed from n to n/4.
> 4. Execute transform algorithm on double primitives instead of on class Complex.
> New instances of Complex are instantiated each time a simple arithmetic operation is
performed on the Complex variables. Much time is lost to object creation and initialisation.

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